List of top Mathematics Questions asked in AP EAPCET

If $ O $ is the origin and $ P, Q $ are points on the line $ 3x + 4y + 15 = 0 $ such that $ OP = OQ = 9 $, then the area of $ \triangle OPQ $ is:

The vector equation of any plane passing through the line of intersection of the planes $ \bar{r} \cdot \bar{n}_1 = q_1 $ and $ \bar{r} \cdot \bar{n}_2 = q_2 $ is given by $ \bar{r} \cdot (\bar{n}_1 + \lambda \bar{n}_2) = q_1 + \lambda q_2 $ for $ \lambda \in \bar{R} $. The vector equation of a plane passing through the point $ 2\bar{i} - 3\bar{j} + \bar{k} $ and the line of intersection of the planes $ \bar{r} \cdot (\bar{i} - 2\bar{j} + 3\bar{k}) = 5 $, $ \bar{r} \cdot (3\bar{i} + \bar{j} - 2\bar{k}) = 7 $ is

Let $ \bar{a}, \bar{b}, \bar{c} $ be three non-coplanar vectors. Then the point of intersection of the line joining the points $ \mathbf{a} + \bar{b} + \bar{c} $, $ \bar{a} - \bar{b} + 3\bar{c} $ and the line joining the points $ 2\bar{a} - \bar{b} + \bar{c} $, $ \bar{a} - 2\bar{b} + 4\bar{c} $ is
In $ \triangle ABC $, the expression $ \frac{a}{s-a} + \frac{b}{s-b} + \frac{c}{s-c} $ is equivalent to:
In $ \triangle ABC $, if $ r = 1 $, $ R = 4 $, and $ \Delta = 8 $, then \[ \frac{1}{ab} + \frac{1}{bc} + \frac{1}{ca} = \]
If $ \cos A + \cos B + \cos C = 0 $ and $ \sin A + \sin B + \sin C = 0 $, then $ \cos(A - B) = $
If $ P = \tan 15^\circ + \cot 15^\circ $, $ Q = \tan 22\frac{1}{2}^\circ + \cot 22\frac{1}{2}^\circ $, and $ R = \sin 54^\circ + \sin 18^\circ $, then their ascending order is
The greatest term in the expansion of $ (1+x)^{15} $, when $ x = \frac{1}{2} $ is
When $ x $ is so small that its square and its higher powers may be neglected, then the value of $ \frac{(1 + \frac{3}{4}x)^{-4} \sqrt{(3 + x)}}{\sqrt{(3 - x)^3}} $ is approximately equal to
If $ 3 + i $ and $ 2 - \sqrt{3} $ are the roots of the equation $ f(x) = a_0 + a_1 x + a_2 x^2 + ... + a_n x^n $, where $ a_0, a_1, ..., a_n \in \mathbb{Z} $, then the least value of $ n $ and the value of $ a_0 $ are respectively:
If the roots of the equation \[ 6x^3 - 11x^2 + 6x - 1 = 0 \] are in harmonic progression, then the roots of \[ x^3 - 6x^2 + 11x - 6 = 0 \] will be in
If $ z_1 = 2 + 3i $, $ z_2 = 4 - 5i $, and $ z_3 $ are three points in the Argand plane such that $ 5z_1 + xz_2 + yz_3 = 0 $ (where $ x, y \in \mathbb{R} $) and $ z_3 $ is the midpoint of the line segment joining the points $ z_1 $ and $ z_2 $, then find $ x + y $.
If $ 1, \omega, \omega^2 $ are the cube roots of unity, then the roots of the equation $ 8z^3 - 12z^2 + 6z - 28 = 0 $ are:
The rank of the matrix \[ \begin{pmatrix} 1 & 0 & 2 \\ 0 & 1 & -2 \\ 1 & -1 & 4 \\ 2 & 2 & 8 \\ \end{pmatrix} \] is

Let $ A = \begin{bmatrix} 2 & 1 & 3 & -1 \\1 & -2 & 2 & -3 \end{bmatrix}, B = \begin{bmatrix} 2 & 1 & 0 & 3 \\1 & -1 & 2 & 3 \end{bmatrix} $, and the equation $ 2A + 3B - 5C = 0 $. Find the matrix $ C $.

The number of ordered pairs $ (x, y) $ for which $ A = \begin{pmatrix} 1 & 2 & 1 \\ 2 & 2 & x \\ y & 1 & 2 \end{pmatrix} $ is a singular and symmetric matrix is:
The domain of the function $ y = f(x) $, where $ x $ and $ y $ are related by $ 2^x + 2^y = 2 $, is:
The range of the function $ f(x) = \begin{cases} 4x - 1, & x>3 \\ x^2 - 2, & -2 \leq x \leq 3 \\ 3x + 4, & x<-2 \end{cases} $ is:

At $ x = \frac{\pi^2}{4} $, $ \frac{d}{dx} \left( \operatorname{Tan}^{-1}(\cos \sqrt{x}) + \operatorname{Sec}^{-1}(e^x) \right) = $
At $ x = \frac{\pi^2}{4} $, $ \frac{d}{dx} \left( \operatorname{Tan}^{-1}(\cos \sqrt{x}) + \operatorname{Sec}^{-1}(e^x) \right) = $

The particular solution of the differential equation \[ \frac{dx}{dy} = \frac{\sin y(1 + y \cot y)}{x \log(x^2 e)}, \quad y(1) = 0 \] Options:
Let $ a $ and $ b $ be arbitrary constants and $ C $ be a fixed constant. If $ y = ae^{2x} + bxe^{2x} + C $ is the general solution of a differential equation, then the order of that differential equation is:
The differential equation \[ y^2 \, dx + (3xy - 1) \, dy = 0 \] is:
$ \int_{0}^{\frac{\pi}{2}} \frac{\sum_{n=0}^{4} \sin \left( \frac{n\pi}{4} + x \right)}{\cos x + \sin x} dx = $
If $ \int_{n}^{n+1} g(x) \, dx = n^2 $, $ \forall n \in Z $, then the value of $ \int_{-3}^{3} g(x) \, dx $ is
$\int e^{-2x} \left( \frac{1 - \sin 2x}{1 + \cos 2x} \right) dx =$